Answer:
Step-by-step explanation:
x + y = 7 ------------(I)
y = 7 - x ------------(II)
x + 2y = 11 --------------(III)
Substitute y = 7 - x in equation (III)
x + 2 * (7 -x) = 11
x + 2*7 - 2*x = 11
x + 14 - 2x = 11
x - 2x + 14 = 11
- x + 14 = 11
Subtract 14 from both side
-x = 11 - 14
-x = -3
Multiply both sides by (-1)
x = 3
Substitute x=3 in equation (II)
y = 7 - 3
y = 4
Margin of error is important in determining the probability as it gives realistic data for the distribution. The formula to be followed for margin of error is m% = z* sqrt (p*(1-p))/n where p is the % positive outcome, n is the sample size and z* is a constant dependent to % confidence level. Substituting, m% = z* (0.03). Level of confidence is not given but assuming at95% CF, m% = 6%
Answer:
Prove set equality by showing that for any element , if and only if .
Example:
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Step-by-step explanation:
Proof for for any element :
Assume that . Thus, and .
Since , either or (or both.)
- If , then combined with , .
- Similarly, if , then combined with , .
Thus, either or (or both.)
Therefore, as required.
Proof for :
Assume that . Thus, either or (or both.)
- If , then and . Notice that since the contrapositive of that statement, , is true. Therefore, and thus .
- Otherwise, if , then and . Similarly, implies . Therefore, .
Either way, .
Therefore, implies , as required.
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